Algebra 2 Cheat Sheets!
(shhhhhh….)
Graphing Absolute Value equations (Cheat Sheet)
Steps:
1: set inside = to zero.
2: solve for x.
3: create a table with the found x value in the middle.
4: Plug x back into the equation to find y. (This is the vertex coordinate.)
5: choose 2 more x values, one on either side of the x you found.
6: Find y values.
7: Graph 3 points.
Example:
1:
2:
5:
Graph y = |x + 5|
x+5=0
x = -5
3:
6:
(Absolute Value)
4:
7: Plot and connect.
Graphing Quadratics (Cheat Sheet)
Steps:
1: set inside = to zero.
2: solve for x.
3: create a table with the found x value in the middle.*
4: Plug x back into the equation to find y. (This is the vertex coordinate.)
5: choose 2 more x values, one on either side of the x you found.
6: Find y values.
7: Choose 1 more x value and find its y value.
8: Plot all 4 points.
9: Use symmetry to find a 5th point.
*Note here that our table has more than 3 rows. This is because quadratics, unlike absolute value
equations, do not grow linearly in each direction.
Example:
1:
2:
Graph y = (x - 1)2 - 2
x-1=0
x = 1
6:
3:
4:
7:
9:
(Quadratic)
5:
8:
Graphing Radicals (square roots) Cheat Sheet
Perfect Squares:
0
Example: Graph
Step 1: Make a table:
x
1
+3
4
9
(radical)
y
Step 2: Set “inside” (x – 5) expression equal to each Perfect Square number above….
x–5=0
x–5=1
x–5=4
x–5=9
x=9
x = 14
… and solve for each x.
x=5
x=6
Step 3: Fill in your table with the x values you just found:
x
5
6
9
14
y
Step 4: Find the y values (plug back in).
x
5
6
9
14
y
3
4
5
6
Step 5: Plot points and connect.
How to graph parabolas, radicals and absolute value on the calculator
Function
How to graph on the calculator
Parabola
Y = x2 + x - 2
Y = XTθN ^ 2 + XTθN – 2 GRAPH
Radical
Y=
-2
Y = 2nd x2 XTθN + 3 ) – 2 GRAPH
Absolute Value
Y = |x + 2| - 4
Y = MATH  NUM 1:abs(
XTθN + 2 ) – 4 GRAPH
ENTER
Graph
Where Domain and Range are Infinite
y = Ax2 + Bx + C
Steps:
Example:
Step 1: Identify A, B and C:
Step 2:
Multiply AC. This is your
A=8
:
B = 10 C = 3
(8)(3) =
Step 3:
Factor your Magic Number (ignoring any – signs for now):
1
2
3
4
Step 4a: Follow the flowchart:




24
12
8
6
Step 4b:
Add + and – signs to each pair in your Magic Number factor list, according to the chart.
Step 5:
Question: “Which factor pair adds to get your B?”
+4  +6
Step 6:
Rewrite your trinomial, replacing B with the numbers you boxed:
Step 7:
Add ( ).
(8x2 + 4x) + (6x + 3)
Step 8:
Factor each ( ):
4x(2x + 1) + 3(2x + 1)
hint: Your two ( ) should always be the same. If one is + and one is -, it’s because one of your factors from step 6 was -.
Usually your first ( ) will be the correct one. To check, distribute backwards to see if you get back to step 6. If not,
switch the sign in the 2nd ( ).
Step 9:
Rewrite to finish.
One ( ) is the stuff on the inside.
One ( ) is the stuff on the outside.
(2x + 1)(4x + 3)
Steps to graphing complicated-looking polynomial functions
like y = x(x + 2)(x + 1)
1: Factor the expression, if necessary.
2: Solve to find the zeros.
3: Plot the zeros on the x axis.
4: Determine the degree.
How many x’s in factored form?
If an odd number (1, 3, 5, etc) then degree is odd.
If an even number (2, 4, 6, etc) then the degree is even.
5: Determine the a value.
Is there a – sign to the left of the =? If no, then the a value is +. If yes, then the a value is -.
6: Draw arrows from the leftmost and rightmost zeros, based on the arrow chart.
7: Multiplicity? If no, there is no “bounce”. Continue “snaking through” the zeros.
If “yes” for multiplicity, as in y = (x – 3)2,
(it’s squared) there is a “bounce” off the x axis! 
Example: Graph y = x3 + 3x2 + 2x
1: Factor the expression.
y = x(x2 + 3x + 2)
y = x(x + 2)(x + 1)
2: Solve to find the zeros.
3: Plot the zeros on the x axis.
x = 0, x = -2, x = -1
4 and 5: Determine the degree and a value.
“3 x’s in factored form, so degree 3 (odd)”
“no – to the left of =, so a is +”
6:
Draw arrows from left and right zeros.
7:
No multiplicity, so “snake through” the zeros.
Patterns for graphing


•
•

Quadratic Word Problems
2
y = -16t + vt + h
v = initial upward velocity
h = initial height
Keywords
Meaning
“How long is it in the air?”
“How long until it hits the
ground?”
Find the zeros (roots) by:
•Factoring,
•graphing
or
•Quadratic Formula
“How long until it reaches
maximum height?”
Find x at the vertex.
(axis of symmetry)
X=
“What is its maximum
height?”
Find y at the vertex.
Graphing Calculator
buttons
-Zero Function2nd, TRACE, 2:Zero
-Max Function2nd, TRACE, 4:Maximum
-Max Function2nd, TRACE, 4:Maximum
“How high is it after x
seconds?”
Find the y coordinate
(height) at the given x
coordinate (time).
(Plug the given x back into
the equation to find y)
-Value Function2nd, TRACE, 1:Value, type in
given x value
Common Graphing Calculator Situations
Problem
I get “ERR:INVALID DIM 1:Quit”
when I try to graph something.
Solution
Y =  Plot1 ENTER (should be Plot1, not black)
SEE THE GRAPH’S ORIGIN
I can’t see the origin.
The origin is off center.
ZOOM 6:ZStandard
The graph is too small.
The graph is too zoomed out.
The graph is too zoomed in.
Where am I?
SEE TO THE RIGHT OR LEFT
I need to see a part of the graph that WINDOW
is out of the window.
Change: Xmin=
Xmax=
Ymin=
Ymax=
to fit what you want to see.
Y-INTERCEPT?
2
FIND THE VERTEX (MINIMUM)
What is the lowest point on the
graph?
nd
TABLE
GRAPH Look for where x = 0
Adjust window to see min point.
2
nd
CALC
TRACE 3:minimum
Left Bound? Arrow left of the min point ENTER
Right Bound? Arrow right of the min point ENTER
Guess? ENTER
FIND THE VERTEX (MAXIMUM)
What is the highest point on the
graph?
Adjust window to see max point.
2
nd
CALC
TRACE 4:maximum
Left Bound? Arrow left of the max point ENTER
Right Bound? Arrow right of the max point ENTER
Guess? ENTER
X-INTERCEPTS? ZEROS?
Where does the graph cross the x
axis?
What are the zeros?
What are the roots?
Adjust window to see one or both x-intercepts.
2
nd
CALC
TRACE 2:zero
Left Bound? Arrow left of one x-intercept ENTER
Right Bound? Arrow right of same x-intercept ENTER
Guess? ENTER
Repeat for other x-intercept(s).
SOLUTION? INTERSECTION?
Where do 2 lines intersect?
What is the solution to this system of
equations?
DOMAIN
What is the domain?
RANGE
What is the range?
CALC
2 TRACE 5:intersect
First curve? Arrow left of intersection ENTER
Right Bound? Arrow right of intersection ENTER
Guess? ENTER
nd
Look at the graph, read and record x values from left
to right.
If there is a maximum point:
(-∞, maximum point y value]
If there is a minimum point:
[minimum point y value, ∞)
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